Backmixed reactors

In this case, Vr is the volume of each individual reactor in the battery. In modeling a reactor, n is empirically determined based on the extent of reactor backmixing obtained from tracer studies or other experimental data. In general, the number of stages n required to approach an ideal PFR depends on the rate of reaction (e.g., the magnitude of the specific rate constant k for the first-order reaction above). As a practical matter, the conversion for a series of stirred tanks approaches a PFR for n > 6. 

In the model of the mixer, the mixing of the streams at the column inlet is taken into account. The residence-time behavior of the piping can be described as a plug-flow reactor. Backmixing effects outside the column can be described by an ideal stirrer tank (Fig. 9.9). 

Let us consider the mass balance of two kinds of three-phase reactors bubble columns and tube reactors with a plug flow for the gas and the liquid phases, and stirred tank reactors with complete backmixing. Modeling concepts can be implemented in most existing reactors backmixing is typical for slurry reactors, bubble columns, and stirred tank reactors, whereas plug flow models describe the conditions in a trickle bed reactor. The interface between the gas and the liquid is supposed to be surroimded by gas and liquid films. Around the catalyst particles, there also exists a liquid film. In gas and liquid films, physical diffusion, but no chemical reactions, is assumed to take place. A volume element is illustrated in Figure 6.15. 

Fresh butane mixed with recycled gas encounters freshly oxidized catalyst at the bottom of the transport-bed reactor and is oxidized to maleic anhydride and CO during its passage up the reactor. Catalyst densities (80 160 kg/m ) in the transport-bed reactor are substantially lower than the catalyst density in a typical fluidized-bed reactor (480 640 kg/m ) (109). The gas flow pattern in the riser is nearly plug flow which avoids the negative effect of backmixing on reaction selectivity. Reduced catalyst is separated from the reaction products by cyclones and is further stripped of products and reactants in a separate stripping vessel. The reduced catalyst is reoxidized in a separate fluidized-bed oxidizer where the exothermic heat of reaction is removed by steam cods. The rate of reoxidation of the VPO catalyst is slower than the rate of oxidation of butane, and consequently residence times are longer in the oxidizer than in the transport-bed reactor. 

Mixing of product and feed (backmixing) in laboratory continuous flow reactors can only be avoided at very high length-to-diameter (aspect) ratios. This was observed by Bodenstein and Wohlgast (1908). Besides noticing this, the authors also derived the mathematical expression for reaction rate for the case of complete mixing. 

Recycle reactors at that time were called Backmix Reactors. They were correctly considered the worst choice for the production of a reactive intermediate, yet the best for kinetic studies. The aim of the kinetic study for ethylene oxidation was to maximize the quality of the information, leaving the optimization of production units for a later stage in engineering studies. The recycle reactors could provide the most precise results at well defined conditions even if at somewhat low selectivity to the desired product. 

A continuous flow stirred tank reactor (CFSTR) differs from the batch reactor in that the feed mixture continuously enters and the outlet mixture is continuously withdrawn. There is intense mixing in the reactor to destroy any concentration and temperature differences. Heat transfer must be extremely efficient to keep the temperature of the reaction mixture equal to the temperature of the heat transfer medium. The CFSTR can either be used alone or as part of a series of battery CFSTRs as shown in Figure 4-5. If several vessels are used in series, the net effect is partial backmixing. 

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

A CSTR is a deliberately backmixed reactor and, in principle, its effluent temperature and composition are the same as the reactor contents. With an ideal CSTR, the feed blends instantaneously with the uniform reactor contents. In actual practice, of course, we find that feed blending time may be protracted, and varying degrees of segregation, short circuiting and stagnation exist in the reactor contents. 

It is likely that some backmixing occurs, especially in the first reactor where fluid viscosities are relatively low. As polymerization proceeds and viscosity increases, the stratified layer condition cited above is gradually approached. 

The rubber phase particles are formed in the first reactor and their average size is also largely determined by conditions existing there. The Ruffing et al patent (27)implies that the first reactor operates significantly backmixed at temperatures between 85 and 130°C with sufficient agitation to maintain the rubber phase uniformly dispersed with a 2-to 25-micron particle... 

Gas phase olefin polymerizations are becoming important as manufacturing processes for high density polyethylene (HOPE) and polypropylene (PP). An understanding of the kinetics of these gas-powder polymerization reactions using a highly active TiCi s catalyst is vital to the careful operation of these processes. Well-proven models for both the hexane slurry process and the bulk process have been published. This article describes an extension of these models to gas phase polymerization in semibatch and continuous backmix reactors. 

The kinetic models for the gas phase polymerization of propylene in semibatch and continuous backmix reactors are based on the respective proven models for hexane slurry polymerization ( ). They are also very similar to the models for bulk polymerization. The primary difference between them lies in the substitution of the appropriate gas phase correlations and parameters for those pertaining to the liquid phase. 

Continuous Model "C0NGAS". This model predicts performance of an ideal continuous wellstirred polyreactor. The model system consists of a continuous backmix reactor in which the total powder volume is held constant. There are four inlet streams 1) Makeup of pure propylene, 2) Catalyst feed, 3) Hydrogen feed, and 4) Recycle. The single effluent powder stream is directed through a perfect separator that removes all solids and polymer and then the gases are recycled to the reactor. The makeup propylene is assumed to disperse perfectly in the well-mixed powder. 

For all likely operating conditions, (ie., for t < X), the appropriate values of the concentration and the polymerization rate constant are the values calculated at t = t ( 2). To prove this, the exit age distribution function for a backmix reactor was used to weight the functions for Cg and kj and the product was integrated over all exit ages (6). It is enlightening at this point to compare equation 18 with one that describes the yield attainable in a typical laboratory semibatch reactor at comparable conditions. ... 

The yield that can be attained by a semibatch process is generally higher because the semibatch run starts from scratch, with maximum values of both variables Cg (o) = Cg and k] (o) = k . However, the yield from a continuous run in which t equals the batch time is governed by the product of Cg (t) and kj (t), so > and k (t) = k °. Because neither of these conditions is likely to be fulfilled completely, a continuous polymerization in a backmix reactor will probably always fail to attain the Y attainable by a semibatch reactor at the same t. However, several backmix reactors in series will approach the behavior of a plug flow continuous reactor, which is equivalent to a semibatch reactor. 

Continuous Simulation, C0NGAS. There are no published data available on propylene continuous polymerization suitable to check the accuracy of the C0NGAS model. However, there is an equation for yield vs. time published by Wisseroth (3 ) for a completely backmixed continuous reactor ... 

Figure 6. Simulation of a continuous backmix reactor (propylene gas phase polymerization—kg° = 0,0249 cm/sec, X = 9.68 hr, 400 psia reactor gas composition—99% CsH6,1% inerts)...

Table II summarizes the yields obtained from the CONGAS computer output variable study of the gas phase polymerization of propylene. The reactor is assumed to be a perfect backmix type. The base case for this comparison corresponds to the most active BASF TiC 3 operated at almost the same conditions used by Wisseroth, 80 C and 400 psig. Agitation speed is assumed to have no effect on yield provided there is sufficient mixing. The variable study is divided into two parts for discussion catalyst parameters and reactor conditions. The catalyst is characterized by kg , X, and d7. Percent solubles is not considered because there is presently so little kinetic data to describe this. The reactor conditions chosen for study are those that have some significant effect on the kinetics temperature, pressure, and gas composition.

Yields from a Continuous Backmix Reactor, Simulated with C0NGAS... 

The effects of diffusion and catalyst decay cause yields from a continuous backmix reactor to be 25 to 30% lower than from a semibatch reactor at the same residence time. This yield penalty can be reduced by staging backmix reactors in series. 

These boundary conditions are really quite marvelous. Equation (9.16) predicts a discontinuity in concentration at the inlet to the reactor so that ain a Q+) if D >0. This may seem counterintuitive until the behavior of a CSTR is recalled. At the inlet to a CSTR, the concentration goes immediately from to The axial dispersion model behaves as a CSTR in the limit as T) — 00. It behaves as a piston flow reactor, which has no inlet discontinuity, when D = 0. For intermediate values of D, an inlet discontinuity in concentrations exists but is intermediate in size. The concentration n(O-l-) results from backmixing between entering material and material downstream in the reactor. For a reactant, a(O-l-) [Pg.332]

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